Safety stock amount calculation method, safety stock amount calculation device, reorder point calculation method, reorder point calculation device, and order quantity calculation method

ABSTRACT

A safety stock amount calculation method includes calculating a probability Pb that a delivery time for a certain commodity required by a customer is shorter than its lead time L, calculating an average value LL of a difference between the lead time L and the customer&#39;s required delivery time when the lead time L exceeds the customer&#39;s required delivery time, correcting an inventory adjustment period N by using the average value LL, and calculating a safety stock amount SS by the equations SS=PB×k×(√{square root over ( )}N×F)×σ, wherein σ is a standard deviation of demand for the commodity, N is a corrected inventory adjustment period, Pb is a probability, F is a shipment frequency, and k is a safety coefficient.

BACKGROUND OF THE INVENTION

1. Technical Field

The present invention relates to a safety stock amount calculationmethod and a safety stock amount calculation device, and moreparticularly to, a technique effectively applied to a safety stockamount calculation processing in a system in which inventory managementis performed based on a projected inventory.

2. Background Art

A method of calculating a safety stock level based on a standarddeviation of past shipments, a lead time L, a safety coefficient k orthe like has been known. In this method, a safety stock amount SS iscalculated by the following [Equation 1]

SS=kσ′

(σ′=√{square root over (stock adjustment period×shipmentfrequency)}×standard deviation of demand σ  [Equation 1]

Where, the demand standard deviation σ is calculated from daily demandamount and shows variation of the daily demand with respect to anaverage demand. The fact that collective stochastic phenomena generallyapproximates to a normal distribution (central limit theorem) is known,and a demand amount is considered to also conform to a normaldistribution in most cases. Here, assuming that a daily standarddeviation is σ, a standard deviation per N days is represented asfollows due to additivity of variance:

√{square root over (N)}×σ

Therefore, in the [Equation 1], the square root of (inventory adjustmentperiod×shipment frequency) is used.

The safety coefficient k represents the level of a permissible stockoutrate and is determined depending on how much uncertainty such as demandfluctuation or prediction error is taken into consideration. The safetycoefficient k is set based on a target ratio of service S. For example,a safety coefficient of 1.65 is obtained from a normal distributiontable of quantity demanded when a ratio of service is 95% (95% of demandis met; permissible stockout rate 5%).

The inventory adjustment period is the length of a period during which aresponse to the customer's order must be made with a quantitycorresponding to a single order. The inventory adjustment period is thelead time L itself in the case of an inventory management according toan order-point system, whereas in the case of an inventory managementaccording to a periodic ordering system, the inventory adjustment periodbecomes a period obtained by adding an ordering cycle M to the lead timeL. The shipment frequency denotes the number of orders made in theinventory adjustment period. In the case where orders are made threetimes per ten days, for example, a value of 0.3 or the like is set asthe shipment frequency. When the demand standard deviation σ iscalculated in units of a week or month, the time unit of the lead time Lor ordering cycle M is correspondingly changed.

Recently, in companies' core information processing systems, an ERP(Enterprise Resource Planning) package that processes informationrelated to various management tasks including inventory management, suchas, accounting management, product management, sales management orpersonnel management distributed within the company in an integratedmanner is gaining acceptance. In the ERP package, task modules such asinventory management are designed with an integrated database havingdaybook-type features as a central core, wherein each of the taskmodules independently functions in general. Of the task modules, theinventory management module adopts a so-called “MRP” (MaterialRequirements Planning). In the MRP, a production plan is drawn up withthe attention paid to the required amount and period of materials basedon a relationship between parts of the product and lead time, andrequired items or the like are ordered based on a projected inventorywhich is a predicted value of projected inventory amount.

In the ERP package described above, inventory management is practiced asfollows. That is, calculation methods of the reorder point and constantorder quantity are previously defined in the case of an order-pointsystem, and a calculation method of the order quantity is previouslydefined in the case of a periodic ordering system, and a user sidemanages a reorder task by appropriately inputting numeric values. Thereorder point or order quantity is determined using the aforementionedsafety stock amount. In the order-point system, “reorder point=minimumstock=average demand during inventory adjustment period (during leadtime L)+safety stock amount” is satisfied. On the other hand, in thecase of the periodic ordering system, “order quantity=commodity amountto be used during inventory adjustment period+safety stockamount−current stock amount−current order remaining amount” issatisfied.

However, the safety stock amount calculation method as described aboveis a method that calculates a safety stock amount obtained in the casewhere orders are made with reference to the stock amount and reorderpoint in the time when the orders are being made. Therefore, the abovesafety stock amount calculation method does not always adapt to aprojected inventory-based system. For the above reason, when thecalculation values obtained according to the conventional method areused in the system such as the ERP package in which inventory managementis carried out based on a projected inventory, the safety stock amountmay become too small or too large, with the result that it is difficultto set a proper reorder point or order quantity. On the EPR software,therefore, calculated values obtained according to the conventionalmethod are input as the safety stock amount with the knowledge thataccuracy may be decreased, or the values obtained by appropriatelycorrecting calculated values based on the seat-of-the-pants estimate ofa person in charge are input as the safety stock amount, failing tobring out system capability. Naturally, it is of high importance toovercome these problems.

An object of the present invention is to provide a safety stock amountcalculation method and a safety stock amount calculation device thatconform to the system that carries out inventory management based on aprojected inventory.

SUMMARY OF THE INVENTION

A safety stock amount calculation method according to the presentinvention that calculates a safety stock amount SS based on a demandstandard deviation σ for a certain commodity, an inventory adjustmentperiod N calculated from a lead time L of the commodity or itscomponents and a safety coefficient k that denotes the level of a ratioof service S for demand, is characterized by comprising the steps of:calculating a probability Pb that a delivery time for the commodityrequired by a customer is shorter than the lead time L; calculating anyof an average value, median, mode, experimental value of the differencebetween the lead time L and the customer's required delivery time, and avalue obtained by subtracting the minimum value of the customer'srequired delivery time from the maximum value of the lead time L as arepresentative value LL of the difference between the lead time L andthe customer's required delivery time in the case where the lead time Lhas exceeded the customer's required delivery time; correcting theinventory adjustment period N to the representative value LL or thevalue obtained by adding an ordering cycle M for the commodity to therepresentative value LL; and calculating the safety stock amount SSbased on the standard deviation σ, corrected inventory adjustment periodN, probability Pb and safety coefficient k.

The calculation method according to the present invention corrects theinventory adjustment period N using the representative value LL as wellas calculates the safety stock amount SS using the short delivery timeratio Pb. Therefore, it is possible to set the practical safety stockamount that meets occurrence of the case where a response to thecustomer's order must be made with the safety stock. Since the safetystock amount calculation method according to the present invention is acalculation method that uses achievement data such as the representativevalue LL and the short delivery time ratio Pb, it is possible to copewith the case where an order of commodity and the like is made based ona projected inventory, making it possible to adequately set the safetystock amount of commodity and the like in the ERP package or the like.

In the safety stock amount calculation method, the step of calculatingthe safety stock amount SS may calculate the safety stock amount SSusing the following equation:

SS=Pb×k×√{square root over (N)}×σ

A safety stock amount calculation method according to the presentinvention that calculates a safety stock amount SS based on a demanddeviation σ for a certain commodity, an inventory adjustment period Ncalculated from a lead time L of the commodity or its components and asafety coefficient k that denotes the level of a ratio of service S fordemand, is characterized by comprising the steps of: calculating thestandard deviation σ based on demand data for the commodity to beobtained in the case where the lead time L has exceeded a customer'srequired delivery time; calculating any of an average value, median,mode, experimental value of the difference between the lead time L andthe customer's required delivery time, and a value obtained bysubtracting the minimum value of the customer's required delivery timefrom the maximum value of the lead time L as a representative value LLof the difference between the lead time L and the customer's requireddelivery time in the case where the lead time L has exceeded thecustomer's required delivery time; correcting the inventory adjustmentperiod N to the representative value LL or the value obtained by addingan ordering cycle M for the commodity to the representative value LL;and calculating the safety stock amount SS based on the standarddeviation σ, corrected inventory adjustment period N, and safetycoefficient k.

In the safety stock amount calculation method, the step of correctingthe inventory adjustment period N may correct the inventory adjustmentperiod N using the representative value LL in place of the lead time Lunder a fixed order quantity system, and may correct the inventoryadjustment period N using the value obtained by adding an ordering cycleM to the representative value LL in place of the lead time L under aperiodic ordering system.

Further, in the safety stock amount calculation method, the correctedinventory adjustment period N may be multiplied by a shipment frequencyF. Furthermore, the representative value LL may be an average of thedifference between the lead time L and customer's required deliverytime. In addition, the calculation method may be applied to a systemthat performs inventory management based on a projected inventory whichis the prediction value of a projected inventory amount. The term“inventory management” used here is a concept including productmanagement involving a commodity procurement activity.

A safety stock amount calculation device according to the presentinvention that calculates a safety stock amount SS based on a pastdemand deviation σ for a certain commodity, an inventory adjustmentperiod N calculated from a lead time L of the commodity or itscomponents and a safety coefficient k that denotes the level of a ratioof service S for demand, is characterized by comprising: a shortdelivery time ratio calculation section that calculates a probability Pbthat a delivery time for the commodity required by a customer is shorterthan the lead time L; an average number of days exceeding delivery timecalculation section that calculates any of an average value, median,mode, experimental value of the difference between the lead time L andthe customer's required delivery time, and a value obtained bysubtracting the minimum value of the customer's required delivery timefrom the maximum value of the lead time L as a representative value LLof the difference between the lead time L and the customer's requireddelivery time in the case where the lead time L exceeds the customer'srequired delivery time; an inventory adjustment period correctionsection that corrects the inventory adjustment period N to therepresentative value LL or the value obtained by adding an orderingcycle M for the commodity to the representative value LL; and a safetystock amount calculation section that calculates the safety stock amountSS based on the standard deviation σ, corrected inventory adjustmentperiod N, short delivery time ratio Pb and safety coefficient k.

A safety stock amount calculation device according to the presentinvention allows an inventory adjustment period correction section tocorrect an inventory adjustment period N using the representative valueLL as well as allows a short delivery time ratio calculation section tocalculate a short delivery time ratio Pb to thereby calculate a safetystock amount SS. Thus, it is possible to set the practical safety stockamount that meets occurrence of the case where a response to thecustomer's order must be made with the safety stock. Further, since thesafety stock amount calculation device according to the presentinvention calculates the safety stock amount using achievement data ofthe representative value LL and the short delivery time ratio Pb, it ispossible to cope with the case where an order of commodity and the likeis made based on a projected inventory, making it possible to adequatelyset the safety stock amount of commodity and the like in the ERP packageor the like.

A safety stock amount calculation device according to the presentinvention that calculates a safety stock amount SS based on a pastdemand deviation σ for a certain commodity, an inventory adjustmentperiod N calculated from a lead time L of the commodity or itscomponents and a safety coefficient k that denotes the level of a ratioof service S for demand, is characterized by comprising: a demandstandard deviation calculation section that calculates the standarddeviation σ based on demand data for the commodity to be obtained in thecase where the lead time L has exceeded a customer's required deliverytime; an average number of days exceeding delivery time calculationsection that calculates any of an average value, median, mode,experimental value of the difference between the lead time L and thecustomer's required delivery time, and a value obtained by subtractingthe minimum value of the customer's required delivery time from themaximum value of the lead time L as a representative value LL of thedifference between the lead time L and the customer's required deliverytime in the case where the lead time L exceeds the customer's requireddelivery time; an inventory adjustment period correction section thatcorrects the inventory adjustment period N to the representative valueLL or the value obtained by adding an ordering cycle M for the commodityto the representative value LL; and a safety stock amount calculationsection that calculates the safety stock amount SS based on the standarddeviation σ, corrected inventory adjustment period N, and safetycoefficient k.

The safety stock amount calculation device may further include a meansfor inputting the lead time L and ratio of service S and a means fordisplaying the safety stock amount SS. Note that the representativevalue LL may be an average of the difference between the lead time L andcustomer's required delivery time. Further, the safety stock amountcalculation device may further include a reorder point calculationsection that calculates a reorder point O by adding a value obtained bymultiplying a demand average A and the representative value LL to thesafety stock amount SS. Further, the safety stock amount calculationdevice may further include an order quantity calculation section thatadds an amount of the commodity or its components to be used in theperiod obtained by adding the representative value LL and an orderingcycle M to the safety stock amount SS and subtracts, from the obtainedvalue, a current stock amount and current order remaining amount tocalculate an order quantity O′.

A safety stock amount calculation program according to the presentinvention allows, in order to calculate a safety stock amount SS, acomputer to function as: a means for calculating a commodity demandstandard deviation σ related to demand for a certain commodity; a meansfor calculating a probability Pb that a delivery time for the commodityrequired by a customer is shorter than the lead time L of the commodityor its components; a means for calculating any of an average value,median, mode, experimental value of the difference between the lead timeL and the customer's required delivery time, and a value obtained bysubtracting the minimum value of the customer's required delivery timefrom the maximum value of the lead time L as a representative value LLof the difference between the lead time L and the customer's requireddelivery time in the case where the lead time L exceeds the customer'srequired delivery time; a means for correcting an inventory adjustmentperiod N to the representative value LL or the value obtained by addingan ordering cycle M of the commodity to the representative value LL; anda means for calculating the safety stock amount SS based on the standarddeviation σ, corrected inventory adjustment period N, probability Pb anda safety coefficient k that denotes the level of a ratio of service Sfor demand.

A safety stock amount calculation program according to the presentinvention allows, in order to calculate a safety stock amount SS, acomputer to function as: a means for calculating a commodity demanddeviation σ related to demand for a certain commodity based on data tobe obtained in the case where the lead time L of the commodity or itscomponents has exceeded the customer's required delivery time; a meansfor calculating any of an average value, median, mode, experimentalvalue of the difference between the lead time L and the customer'srequired delivery time, and a value obtained by subtracting the minimumvalue of the customer's required delivery time from the maximum value ofthe lead time L as a representative value LL of the difference betweenthe lead time L and the customer's required delivery time in the casewhere the lead time L exceeds the customer's required delivery time; ameans for correcting an inventory adjustment period N to therepresentative value LL or the value obtained by adding an orderingcycle M of the commodity to the representative value LL; and a means forcalculating the safety stock amount SS based on the standard deviationσ, corrected inventory adjustment period N, and a safety coefficient kthat denotes the level of a ratio of service S for demand.

On the other hand, a reorder point calculation method according to thepresent invention is characterized by comprising calculating a reorderpoint O by adding a value obtained by multiplying a demand average A andthe representative value LL to a safety stock amount SS calculated bythe aforementioned safety stock amount calculation method. Further, aorder quantity calculation method according to the present invention ischaracterized by comprising adding an amount of the commodity or itscomponents to be used in the period obtained by adding therepresentative value LL and an ordering cycle M to the safety stockamount SS calculated by the aforementioned safety stock amountcalculation method and subtracting, from the obtained value, a currentstock amount and current order remaining amount to calculate an orderquantity O′.

Next, a safety stock amount calculation method according to the presentinvention is characterized by comprising the steps of: calculating anappearance probability of a certain delivery time for each delivery timebased on the delivery time for a certain commodity required by acustomer and its frequency; calculating an appearance probability of alead time of the commodity or its components; calculating, based on thecustomer's required delivery time and lead time, an effective lead timeT_(i) that denotes the period between the time when it has beenpredicted that the commodity stock will fall below a correspondingreorder point and the time when the commodity has become available afterthe commodity had been ordered based on the prediction that thecommodity stock would fall below a corresponding reorder point;calculating an appearance probability of the effective lead time T_(i)for each effective lead time T_(i) based on the appearance probabilityof the customer's required delivery time and the appearance probabilityof the lead time; and calculating a safety stock amount ss based on ademand standard deviation σ_(D) for the commodity per unit of period, asafety coefficient k that denotes the level of a ratio of service S fordemand, the effective lead time T_(i) and the appearance probability ofthe effective lead time.

A safety stock amount calculation method according to the presentinvention is characterized by comprising the steps of: calculating anappearance probability of a certain delivery time for each delivery timebased on the delivery time for a certain commodity required by acustomer and its frequency to create a probability distribution g_(j) ofthe customer's required delivery time; calculating an appearanceprobability of a lead time of the commodity or its components to createa probability distribution h_(k) of the lead time; calculating, based onthe customer's required delivery time and lead time, an effective leadtime T_(i) that denotes the period between the time when it has beenpredicted that the commodity stock will fall below a correspondingreorder point and the time when the commodity has become available afterthe commodity had been ordered based on the prediction that thecommodity stock would fall below a corresponding reorder point;calculating an appearance probability of the effective lead time T_(i)for each effective lead time T_(i) based on the probability distributiong_(j) of the customer's required delivery time and the probabilitydistribution h_(k) of the lead time to create a probability distributionf_(i) of the effective lead time; and calculating a safety stock amountss based on a demand standard deviation σ_(D) for a certain commodityper unit of period, a safety coefficient k that denotes the level of aratio of service S for demand, the effective lead time T_(i) and theprobability distribution f_(i) of the effective lead time.

The safety stock amount calculation method according to the presentinvention calculates the appearance probability related to thecustomer's required delivery time and the lead time as well ascalculates the appearance probability of the effective lead time usingthe above calculated values and finally calculates the safety stockamount based on the effective lead time and the appearance probabilitythereof. As a result, it is possible to design a more general inventorymanagement system being based on a projected inventory. Further, thesafety stock amount calculation method of the present invention is acalculation method that uses achievement data, it is possible to copewith the case where an order of commodity and the like is made based ona projected inventory, making it possible to adequately set the safetystock amount of commodity and the like in the ERP package or the like.

In the safety stock amount calculation method, the step of calculatingthe safety stock amount ss may calculates the safety stock amount ssusing the following equation:

SS=k√{square root over (Σf_(i) ²T_(i))}σ_(D)

In the aforementioned safety stock amount calculation method, the stepof calculating the safety stock amount ss may use a demand frequencyF_(D) that denotes an appearance probability of the period during whichdemand per unit of period is not 0. Further, in the aforementionedsafety stock amount calculation method, at least one of the probabilitydistribution of g_(j) of the customer's required delivery time and theprobability distribution h_(k) of the lead time may be a discreteprobability distribution.

Another safety stock amount calculation device according to the presentinvention is characterized by comprising: a delivery time appearanceprobability calculation section that calculates an appearanceprobability of a certain delivery time for each delivery time based onthe delivery time for a certain commodity required by a customer and itsfrequency; a lead time appearance probability calculation section thatcalculates an appearance probability of a lead time of the commodity orits components; an effective lead time calculation section thatcalculates, based on the customer's required delivery time and leadtime, an effective lead time T_(i) that denotes the period between thetime when it has been predicted that the commodity stock will fall belowa corresponding reorder point and the time when the commodity has becomeavailable after the commodity had been ordered based on the predictionthat the commodity stock would fall below a corresponding reorder point;an effective lead time appearance probability calculation section thatcalculates an appearance probability of the effective lead time T_(i)for each lead time T_(i) based on the appearance probability of thecustomer's required delivery time and the appearance probability of thelead time; and a safety stock amount calculation section that calculatesa safety stock amount ss based on a demand standard deviation σ_(D) fora certain commodity per unit of period, a safety coefficient k thatdenotes the level of a ratio of service S for demand, the effective leadtime T_(i) and the appearance probability of the effective lead time.

Another safety stock amount calculation device according to the presentinvention is characterized by comprising: a probability distribution ofcustomer's required delivery time calculation section that calculates anappearance probability of a certain delivery time for each delivery timebased on the delivery time for a certain commodity required by acustomer and its frequency to create a probability distribution g_(j) ofthe customer's required delivery time; a lead time probabilitydistribution calculation section that calculates an appearanceprobability of a lead time of the commodity or its components to createa probability distribution h_(k) of the lead time; an effective leadtime calculation section that calculates, based on the customer'srequired delivery time and lead time, an effective lead time T_(i) thatdenotes the period between the time when it has been predicted that thecommodity stock will fall below a corresponding reorder point and thetime when the commodity has become available after the commodity hadbeen ordered based on the prediction that the commodity stock would fallbelow a corresponding reorder point; an effective lead time probabilitydistribution calculation section that calculates an appearanceprobability of the effective lead time T_(i) for each lead time Ti basedon the probability distribution g_(j) of the customer's requireddelivery time and the probability distribution h_(k) of the lead time tocreate a probability distribution f_(i) of the effective lead time; anda safety stock amount calculation section that calculates a safety stockamount ss based on a demand standard deviation σ_(D) for a certaincommodity per unit of period, a safety coefficient k that denotes thelevel of a ratio of service S for demand, the effective lead time T_(i)and the probability distribution f_(i) of the effective lead time.

The safety stock amount calculation device according to the presentinvention calculates the appearance probability related to thecustomer's required delivery time and the lead time as well ascalculates the appearance probability of the effective lead time usingthe above calculated values and finally calculates the safety stockamount based on the effective lead time and the appearance probabilitythereof. As a result, it is possible to design a more general inventorymanagement system being based on a projected inventory. Since the methodof the present invention is a calculation method that uses achievementdata, it is possible to cope with the case where an order of commodityand the like is made based on a projected inventory, making it possibleto adequately set the safety stock amount of commodity and the like inthe ERP package or the like.

A safety stock amount calculation program according to the presentinvention allows, in order to calculate a safety stock amount ss of acertain commodity, a computer to function as: a means for calculating,based on a customer's required delivery time and a lead time of thecommodity or its components, an effective lead time T_(i) that denotesthe period between the time when it has been predicted that thecommodity stock will fall below a corresponding reorder point and thetime when the commodity has become available after the commodity hadbeen ordered based on the prediction that the commodity stock would fallbelow a corresponding reorder point; a means for calculating anappearance probability of the effective lead time T_(i) for each leadtime T_(i) based on an appearance probability of the customer's requireddelivery time calculated from the customer's required delivery time andits frequency and an appearance probability of the lead time of thecommodity or its components; and a means for calculating a safety stockamount ss based on a demand standard deviation σ_(D) for the commodityper unit of period, a safety coefficient k that denotes the level of aratio of service S for demand, the effective lead time T_(i) and theappearance probability of the effective lead time.

Another safety stock amount calculation program according to the presentinvention allows, in order to calculate a safety stock amount ss of acertain commodity, a computer to function as: a means for calculating anappearance probability of a certain delivery time for each delivery timebased on the delivery time for a certain commodity required by acustomer and its frequency to create a probability distribution g_(j) ofthe customer's required delivery time; a means for calculating anappearance probability of a lead time of the commodity or its componentsto create a probability distribution h_(k) of the lead time; a means forcalculating, based on the customer's required delivery time and leadtime, an effective lead time T_(i) that denotes the period between thetime when it has been predicted that the commodity stock will fall belowa corresponding reorder point and the time when the commodity has becomeavailable after the commodity had been ordered based on the predictionthat the commodity stock would fall below a corresponding reorder point;a means for calculating an appearance probability of the effective leadtime T_(i) for each lead time T_(i) based on the probabilitydistribution g_(j) of the customer's required delivery time and theprobability distribution h_(k) of the lead time to create a probabilitydistribution f_(i) of the effective lead time; and a means forcalculating a safety stock amount ss based on a demand standarddeviation σ_(D) for the commodity per unit of period, a safetycoefficient k that denotes the level of a ratio of service S for demand,the effective lead time T_(i) and the probability distribution f_(i) ofthe effective lead time.

A reorder point calculation method according to the present invention ischaracterized by comprising calculating a reorder point Q_(RO) based ona safety stock amount ss calculated by the aforementioned safety stockamount calculation method, a representative value DA from which electedany of an average value, median, mode and experimental value of a demandper unit of period, and a marginal lead time L_(M) that denotes aminimum value of the effective lead time to be obtained after thecumulative value of the appearance probability of the effective leadtime T_(i) has exceeded the ratio of service S. In this case, thereorder point Q_(RO) may be calculated by further using a demandfrequency F_(D) that denotes an appearance probability of the periodduring which demand per unit of period is not 0 in addition to thesafety stock amount ss, representative value DA of a demand, andmarginal lead time L_(M).

Another reorder point calculation device according to the presentinvention is characterized by comprising: a delivery time appearanceprobability calculation section that calculates an appearanceprobability of a certain delivery time for each delivery time based onthe delivery time for a certain commodity required by a customer and itsfrequency; a lead time appearance probability calculation section thatcalculates an appearance probability of a lead time of the commodity orits components; an effective lead time calculation section thatcalculates, based on the customer's required delivery time and leadtime, an effective lead time T_(i) that denotes the period between thetime when it has been predicted that the commodity stock will fall belowa corresponding reorder point and the time when the commodity has becomeavailable after the commodity had been ordered based on the predictionthat the commodity stock would fall below a corresponding reorder point;an effective lead time appearance probability calculation section thatcalculates an appearance probability of the effective lead time T_(i)for each lead time T_(i) based on the appearance probability of thecustomer's required delivery time and the appearance probability of thelead time; a safety stock amount calculation section that calculates asafety stock amount ss based on a demand standard deviation σ_(D) forthe commodity per unit of period, a safety coefficient k that denotesthe level of a ratio of service S for demand, the effective lead timeT_(i) and the appearance probability of the effective lead time; and areorder point calculation section that calculates a reorder point Q_(RO)based on the safety stock amount ss, a representative value DA fromwhich elected any of an average value, median, mode, and experimentalvalue of a demand per unit of period, and a marginal lead time L_(M)that denotes a minimum value of the effective lead time to be obtainedafter the cumulative value of the appearance probability of theeffective lead time T_(i) has exceeded the ratio of service S.

Another reorder point calculation device according to the presentinvention is characterized by comprising: a probability distribution ofcustomer's required delivery time calculation section that calculates anappearance probability of a certain delivery time for each delivery timebased on the delivery time for a certain commodity required by acustomer and its frequency to create a probability distribution g_(j) ofthe customer's required delivery time; a lead time probabilitydistribution calculation section that calculates an appearanceprobability of a lead time of the commodity or its components to createa probability distribution h_(k) of the lead time; an effective leadtime calculation section that calculates, based on the customer'srequired delivery time and lead time, an effective lead time T_(i) thatdenotes the period between the time when it has been predicted that thecommodity stock will fall below a corresponding reorder point and thetime when the commodity has become available after the commodity hadbeen ordered based on the prediction that the commodity stock would fallbelow a corresponding reorder point; an effective lead time probabilitydistribution calculation section that calculates an appearanceprobability of the effective lead time T_(i) for each lead time Ti basedon the probability distribution g_(j) of the customer's requireddelivery time and the probability distribution h_(k) of the lead time tocreate a probability distribution f_(i) of the effective lead time; asafety stock amount calculation section that calculates a safety stockamount ss based on a demand standard deviation σ_(D) for a certaincommodity per unit of period, a safety coefficient k that denotes thelevel of a ratio of service S for demand, the effective lead time T_(i)and the probability distribution f_(i) of the effective lead time; and areorder point calculation section that calculates a reorder point Q_(RO)based on the safety stock amount ss, a representative value DA fromwhich elected any of an average value, median, mode and experimentalvalue of a demand per unit of period, and a marginal lead time L_(M)that denotes a minimum value of the effective lead time to be obtainedafter the cumulative value of the appearance probability of theeffective lead time T_(i) has exceeded the ratio of service S.

In the reorder point calculation device, the reorder point calculationsection may calculate the reorder point Q_(RO) by further using a demandfrequency F_(D) that denotes an appearance probability of the periodduring which demand per unit of period is not 0 in addition to thesafety stock amount ss, representative value DA of a demand, andmarginal lead time L_(M).

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a system configuration diagram of a safety stock amountcalculation device according to a first embodiment of the presentinvention;

FIG. 2 is a control block diagram in the calculation device of FIG. 1;

FIG. 3 is a flowchart showing a procedure of a safety stock amountcalculation method performed in the calculation device of FIG. 1;

FIG. 4 is a control block diagram of the safety stock amount calculationdevice according to a second embodiment of the present invention;

FIG. 5 is a flowchart showing a procedure of a safety stock amountcalculation method performed in the calculation device of FIG. 4;

FIG. 6 is an explanatory view showing an example of a discreteprobability distribution g_(j) of a customer's required delivery time;

FIG. 7 is an explanatory view showing an example of a discreteprobability distribution h_(k) of a lead time;

FIG. 8 is a table showing calculation results of an effective lead timeT_(i) in the case of FIGS. 6 and 7; and

FIG. 9 is a table showing results of various calculations using adiscrete probability distribution f_(i) of the effective lead time T_(i)obtained in FIG. 8.

DETAILED DESCRIPTION OF THE INVENTION First Embodiment

Embodiments of the present invention will be described below in detailwith reference to the accompanying drawings. FIG. 1 is a systemconfiguration diagram of a safety stock amount calculation deviceaccording to a first embodiment of the present invention. FIG. 2 is acontrol block diagram in the calculation device of FIG. 1. FIG. 3 is aflowchart showing a procedure of a safety stock amount calculationmethod performed in the calculation device of FIG. 1.

As shown in FIG. 1, the calculation device includes a CPU 1, a memory 2,a storage unit 3, an input unit (input means) 4, and an output unit(output means) 5, which are connected to each other via a bus 6. Thememory 2 stores a safety stock amount calculation program 11, a workarea 12, and a control program 13. The safety stock amount calculationprogram 11, which is executed by the CPU 1, calculates a safety stockamount according to the procedure shown in FIG. 3. The safety stockamount calculation program 11 is an “add-on” program that exists in anERP package as an underlying program or external program, stored in acomputer-readable recording medium, and executed after being read intothe memory 2 via a driving unit. The safety stock amount calculationprogram 11 can be used independently from the ERP package.

The work area 12 is a work area that stores an intermediate result of aprocess based on the safety stock amount calculation program 11. Thecontrol program 13 is a program that controls the entire system. Thatis, the control program 13 controls the storage unit 3, input unit 4,and output unit 5 in an integrated manner to execute the safety stockamount calculation program 11.

The storage unit 3 stores a sales/shipment database (hereinafter,“database” is abbreviated as “DB”) 14, an order DB 15, and a safetycoefficient table 16. The sales/shipment DB 14 stores a pastsales/shipment record related to a certain commodity (products/articles)or components thereof (parts/materials) (hereinafter, referred to as“commodity and the like”). The order DB 15 stores a past order record ofcommodity and the like. The safety coefficient table 16 stores data orfunction indicating a correlation between a ratio of service S andsafety coefficient k.

The input unit 4 is a keyboard, mouse, or the like that serves as a unitfor inputting various data and instructions for the CPU 1. The outputunit 5 is a display or printer that serves as a unit for displayingcalculated safety stock amount, reorder point, order quantity or thelike. Note that the calculation device may be embodied by a personalcomputer and its peripherals.

The CPU 1 has a function means as shown in FIG. 2. More specifically,the CPU 1 roughly includes a basic data computation section 21, acorrection data computation section 22, a safety coefficient calculationsection 23, a safety stock amount calculation section 24, and a reorderpoint and the like calculation section 25. Input to the CPU 1 via theinput unit 4, are a lead time L, an ordering cycle M, a ratio of service(or permissible stockout rate) S or the like. Note that various patternsof the lead time L can be adopted depending on the property of commodityand the like. That is, the lead time L includes not only a procurementlead time indicating a period from order to receipt of a commodity andthe like but also a period obtained by adding a manufacturing/assemblylead time indicating a parts manufacturing/assembly period to theprocurement lead time, and the above period further includingtransportation time, inspection time and the like.

The basic data computation section 21 calculates a demand standarddeviation σ, a demand average A, a shipment frequency F based on data ofthe sales/shipment DB 14. The demand standard deviation σ, demandaverage A, and shipment frequency F are calculated in a demand standarddeviation calculation section 31, a demand average calculation section32, and shipment frequency calculation section 33, respectively. As thestandard deviation σ, an approximate value obtained by multiplying adifference between maximum and minimum values of data by a predeterminedcoefficient (1/d²), which is determined by the number of samples, may beused.

The correction data computation section 22 calculates correction datathat has been not used in a conventional safety coefficient calculationmethod based on input data and data of the order DB 15. That is, aprobability Pb that the customer's required delivery time is shorterthan the lead time L of the parts/materials used in the commodity(hereinafter, abbreviated as “short delivery time ratio” (make to stockratio)) is calculated in a short delivery time ratio calculation section34. Further, the average number of days exceeding the lead time, whichis an average of the difference between the lead time L and thecustomer's required delivery time for the portion that the lead time Lexceeds the delivery time required by the customer (hereinafterabbreviated as average number of days exceeding delivery time), iscalculated as a representative value LL in an average number of daysexceeding delivery time calculation section 35.

Further, an inventory adjustment period N is calculated in an inventoryadjustment period correction section 36. In a conventional calculationmethod, the inventory adjustment period N is, as described above, thelead time L itself in the case where the order-point system is used, andbecomes a period obtained by adding an ordering cycle M to the lead timeL in the case where the periodic ordering system is used. On the otherhand, in the method according to the present invention, the inventoryadjustment period N is corrected by the previously calculated averagenumber of days exceeding delivery time LL, and the obtained value isused as N. That is, as the inventory adjustment period N, the averagenumber of days exceeding delivery time LL (N=LL) is used under the fixedorder quantity system, and the value (N=LL+M) obtained by adding theordering cycle M to the average number of days exceeding delivery timeLL is used under the periodic ordering system.

The safety coefficient calculation section 23 calculates a safetycoefficient k from the safety coefficient table 16 with reference to theratio of service S input via the input unit 4. As described above, whena ratio of service S of 95% is input, the safety coefficient calculationsection 23 calculates k=1.67 based on the safety coefficient table 16created according to a normal distribution table. Note that the presentinvention is also applicable to the case where a demand amount does notexhibit normal distribution. In this case, distribution function of ademand amount is calculated, and the safety coefficient k that satisfiesa desired ratio of service S is calculated based on the calculateddistribution function, for example.

The safety stock amount calculation section 24 calculates a safety stockamount SS based on data obtained in the basic data computation section21 or correction data computation section 22 and the safety coefficientk obtained in the safety coefficient calculation section 23. Here, thesafety stock amount SS is calculated by the following equation:

SS=Pb×k×√{square root over (N×F)}×σ  [Equation 2]

The reorder point and the like calculation section 25 calculates areorder point or an order quantity based on the safety stock amount SSobtained in the safety stock amount calculation section 24. In the caseof the fixed order quantity system, the reorder point and the likecalculation section 25 functions as a reorder point calculation sectionand calculates a reorder point O (O=A×LL+SS). In the case of theperiodic ordering system, the reorder point and the like calculationsection 25 functions as an order quantity calculation section andcalculates an order quantity O′ (O′=commodity amount to be used in(LL+ordering cycle M)+SS−current stock amount−current order remainingamount). Note that the current stock amount and current order remainingamount are input through the input unit 4.

In the calculation device having the configuration described above, thesafety stock amount SS is calculated along the procedure as describedbelow for obtaining the reorder point O and the like. As shown in FIG.3, firstly, a lead time L, ordering cycle M, and ratio of service (orpermissible stockout rate) S are input in steps S1 to S3. The lead timeL is a period from order to receipt of commodity, and e.g. “10 days” orthe like is input as the lead time L. The ordering cycle M is orderinterval set in the periodic ordering system, and e.g.“30 days” or thelike is input as the ordering cycle M. As the ratio of services, “95%”or the like is input as described above.

Next, when inputs of these values have been completed, the CPU 1accesses the safety stock amount calculation program 11 according to thecontrol program 13 and accordingly calculates various fundamental data.In order to calculate the safety stock amount SS, the safety stockamount calculation program 11 allows the CPU (computer) 1 to function asthe demand standard deviation calculation section 31, short deliverytime ratio calculation section 34, average number of days exceedingdelivery time calculation section 35, inventory adjustment periodcorrection section 36, and safety stock amount calculation section 24.

The CPU 1 calculates the safety coefficient k, demand standard deviationσ, demand average A, and shipment frequency F in steps S3 to S7. Thecalculated values are stored in the work area 12 and used in thefollowing computations.

As described above, the safety coefficient k is calculated by the safetycoefficient calculation section 23, which obtains it from the safetycoefficient table 16 with reference to the input ratio of service S. Thedemand standard deviation σ, demand average A, and shipment frequency Fare calculated by the basic data computation section 21 based on data ofthe sales/shipment DB 14. Note that these values (k, σ, A, and F) may bedirectly input through the input unit 4.

After the fundamental data have been calculated, the CPU 1 calculatesvarious correction data. In step S8, the short delivery time ratio Pb iscalculated by the short delivery time ratio calculation section 34. Theshort delivery time ratio Pb denotes a probability that commodity andthe like will not procured in time. For example, in the case where theprobability of “a customer's required delivery time<the lead time L” is30% of the total, according to a past order data, Pb=0.3 is obtained. Asto the short delivery time ratio Pb, user's experimental values may bedirectly input through the input unit 4. For example, when the number ofdata in the order DB 15 is small like the case in the launch time of thesystem, it is impossible to correctly calculate the probability, so thata manual input is required. In this case, at the time point when orderdata has been accumulated to some degree, input mode may appropriatelybe switched to an automatic calculation. Weighting may be applied to theshort delivery time ratio Pb depending on the number of orderedcommodities per order. In this case, when 90 commodities are ordered twotimes as a short delivery time order, and 110 commodities are orderedthree times as a short delivery time order with 100 commodities as areference order number, the Pb is multiplied by 1.08 (=0.9²×1.1³).

The flow advances to step S9, where the average number of days exceedingdelivery time LL is calculated by the average number of days exceedingdelivery time calculation section 35. The average number of daysexceeding delivery time LL denotes the average number of days duringwhich a response to the customer's order must be made with a safetystock and is used for a calculation of the inventory adjustment period Nin the following step S10. The average number of days exceeding deliverytime LL is also calculated based on data of the order DB 15. As to theaverage number of days exceeding delivery time LL, user's experimentalvalues may be directly input through the input unit 4.

In step S10, the inventory adjustment period N is calculated in theinventory adjustment period correction section 36. As described above,the calculation equation of the N differs depending on the orderingsystem. The value of the N may also be input directly through the inputunit 4. After the inventory adjustment period N has been calculated, theflow advances to step S11, where the safety stock amount calculationsection 24 calculates the safety stock amount SS using the above[Equation 2]. As the demand standard deviation σ, a square root of theaverage of the square of the difference between each data value andpredicted value may be used in place of the method in which a square ofthe deviation between each data value and average value is obtained anda square root of the average of the obtained values is used as the σ.

The multiplication of the F (shipment frequency) in the above [Equation2] can be omitted. In order to determine whether the multiplication ofthe F is applied or not, the calculation method of the demand average Aand demand standard deviation σ needs to be changed. That is, as to thedata of the day on which no shipment has been made, the calculation ofthe A or σ is performed on the assumption that the relevant data doesnot exist, not using “0” as the relevant data, in the case where theshipment frequency F is used. Which is to say, since data handlingmethod differs depending on whether the shipment frequency F is appliedor not, the value of the demand average A or demand standard deviation σmentioned here accordingly differs.

The [Equation 2] differs from the [Equation 1] in the following points:{circle around (1)} In the calculation of N, the average number of daysexceeding delivery time LL is used in place of the lead time L. {circlearound (2)} Short delivery time ratio Pb is multiplied. Firstly, as tothe point {circle around (1)}, the safety stock amount is calculatedbased on procurement period from the current time period in theconventional method. On the other hand, in the present invention, thesafety stock amount is calculated using the average number of daysexceeding delivery time LL, that is, an actual compliance period basedon the safety stock amount. For example, in the case where the averagecustomer's required delivery time is 7 days and the inventory adjustmentperiod is 10 days, the safety stock amount corresponding to 3 days isactually required on average. Whereas, according to the conventionalmethod, the safety stock amount corresponding to 10 days is required.That is, in the calculation method according to the present invention,it is possible to calculate the safety stock amount more practicallythan the calculation method simply using the lead time L. In the aboveexample, it is possible to cut out the stock corresponding to 7 days,reducing stock amounts and, thereby, enabling the cost reduction.

As to the point {circle around (2)}, it is possible to determine thesafety stock value in consideration of the actual number of the caseswhere a response to the customer's order must be made with the safetystock by multiplying the value obtained using the N by the Pb, the Nhaving been calculated using the average number of days exceedingdelivery time LL. In this case, if there is no case where “customer'srequired delivery time<lead time L”, Pb=0→SS=0, which means that thereis no need to have the safety stock. On the other hand, if the statewhere “customer's required delivery time<lead time L” always continues,the Pb becomes 1.0, which means that there is a need to have enoughamount of the safety stock to cope with the average number of daysexceeding delivery time LL. Further, if the Pb has a value between theabove two cases, that is, Pb=0.3, for example, it is only necessary tohave enough amount of the safety stock to cope with the 30%. As aresult, it is possible to reduce the safety stock amount by an amountcorresponding to the multiplication of Pb (≦1.0), as compared to theconventional method.

As described above, in the calculation method according to the presentinvention, it is possible to calculate the safety stock amount morepractically by using the average number of days exceeding delivery timeLL in place of the lead time L. Further, it is possible to set thesafety stock amount that meets occurrence of the case where a responseto the customer's order must be made with the safety stock by using theshort delivery time ratio Pb. Since this method is a calculation methodthat uses achievement data of average number of days exceeding deliverytime LL and the short delivery time ratio Pb, it is possible to copewith the case where an order of commodity and the like is made based ona projected inventory, making it possible to adequately set the safetystock amount of commodity and the like in the ERP package or the like.

After the safety stock amount SS has been calculated in the manner asdescribed above, the flow advances to step S12, where the reorder pointO and order quantity are calculated in the reorder point and the likecalculation section 25. At this time, the safety stock amount SS is usedin the calculation of the reorder point O and the like. Therefore, moreaccurate and efficient reorder point and the like can be obtained in thecalculation method according to the present invention. The calculatedreorder point O and the like are displayed on the output unit 5 togetherwith the safety stock amount SS, and a user makes an order of commodityand the like with reference to the calculated results.

In the above embodiment, the safety stock amount SS is calculated usingthe short delivery time ratio Pb. Alternatively, however, it is possibleto calculate the safety stock amount SS without using the short deliverytime ratio Pb, that is, the demand standard deviation σ is calculatedbased on the demand to be obtained on the assumption that the lead timeL exceeds the customer's required delivery time, and the safety stockamount SS is obtained using the calculated σ. In this case, the demandstandard deviation σ is calculated using the data (or only the data)obtained on the assumption that the lead time L actually exceeds thecustomer's required delivery time, which eliminates the need ofcalculating the short delivery time ratio Pb. That is, it is possible tocalculate the safety stock amount SS using the equation obtained byomitting the Pb from the [Equation 2].

In this case, the demand standard deviation calculation section 31calculates the demand standard deviation σ using only the data obtainedon the assumption that the lead time L actually exceeds the customer'srequired delivery time. Further, the safety stock amount calculationsection 24 calculates the safety stock amount SS based on the demandstandard deviation σ calculated here, corrected inventory adjustmentperiod N, shipment frequency F, and safety coefficient k.

Second Embodiment

A safety stock amount calculation device according to a secondembodiment of the present invention will next be described. FIG. 4 is acontrol block diagram of the safety stock amount calculation deviceaccording to the second embodiment of the present invention; and FIG. 5is a flowchart showing a procedure of a safety stock amount calculationmethod performed in the calculation device of FIG. 4. In thisembodiment, the same reference numerals as those in the first embodimentdenote the same parts or means as those in the first embodiment, and thedescriptions thereof will be omitted here.

The calculation device and calculation method according to the secondembodiment have a more general configuration as compared to that of thefirst embodiment. The first embodiment corresponds to a so-calledparticular solution that specifies conditions in the second embodiment.As in the case of the first embodiment, the calculation device accordingto the second embodiment includes the CPU 1, memory 2, storage unit 3,input unit 4, and output unit 5. These components are connected to eachother via bus 6. Input to the CPU 1 via the input unit 4, are thepermissible stockout rate α (or ratio of service S), ordering cycle Mand the like. The CPU 1 has a function means as shown in FIG. 4. Morespecifically, the CPU 1 roughly includes the basic data computationsection 21, a computation data calculation section 26, the safetycoefficient calculation section 23, the safety stock amount calculationsection 24, and the reorder point and the like calculation section 25.

The basic data calculation section 21 calculates a demand standarddeviation per unit of period σ_(D), a demand average (representativevalue) per unit of period DA, and a demand frequency F_(D) based on dataof the sales/shipment DB 14. The demand standard deviation σ_(D) anddemand average DA are calculated respectively in a demand standarddeviation calculation section 41 and demand average calculation section42, where a period such as one day or one month is set as the unit ofperiod.

The demand frequency F_(D) is an appearance probability of the periodduring which demand per unit of period is not 0 and is calculated in ademand frequency calculation section 43. The demand frequency F_(D) isused as a shipment frequency F in terms of the shipment and correspondsto an appearance probability of the day on which the shipment is not 0.The demand frequency F_(D) is used as a production frequency in terms ofthe production quantity and corresponds to an appearance probability ofthe day on which the production quantity is not 0. When the DA or σ_(D)is calculated, it is possible to contain the period during which thedemand is 0 with the F_(D) assumed to be 1.

The computation data calculation section 26 calculates variouscomputation data based on input data or data of the order DB 15.Provided firstly in the computation data calculation section 26 is adelivery time probability distribution calculation section 44 thatcalculates a discrete probability distribution of a customer's requireddelivery time. Although the customer's required delivery time includesvarious periods, such as the very day on which the request has beenmade, several months away, several years away, it falls within a certaindegree of variations in terms of a certain commodity. As a result, anappearance probability of a certain customer's required delivery timecan be represented by a discrete probability distribution defined byg_(j) based on a delivery time of commodity and the like, which is atarget of inventory management, required by a customer DT_(j) and theits required number of times. FIG. 6 is an explanatory view showing anexample of the discrete distribution g_(j) of a customer's requireddelivery time. As can be seen from FIG. 6, the probability that thecustomer's required delivery time DT is 1 day is 0.5; the probabilitythat the delivery time DT is 2 days is 0.3, and the probability that thedelivery time DT is 3 days is 0.2, in which the total sum of theprobability g_(j) becomes 1.

Further provided in the computation data calculation section 26 is alead time probability distribution calculation section (lead timeappearance probability calculation section) 45 that calculates adiscrete probability distribution h_(k) of a lead time. The lead timedenotes a length of the period from which an order of commodity has beenmade or a production order has been released at the time point when ithas been understood that a commodity would be required until theshipment of the commodity or use thereof is enabled after delivery ofthe commodity or completion of the manufacturing of the commodity. Inthe case of purchasing a commodity, a procurement lead time correspondsto the above lead time. In the case of manufacturing a commodity, aproduction lead time corresponds to the above lead time.

Although the lead time also includes various periods, it falls within acertain degree of variations in terms of a certain commodity. As aresult, an appearance probability of a certain lead time can berepresented by a discrete probability distribution defined by h_(k)based on appearance frequency of a lead time LT_(k) of commodity and thelike, which is a target of inventory management. FIG. 7 is anexplanatory view showing an example of the discrete distribution h_(k)of the lead time. As can be seen from FIG. 7, the probability that thelead time LT is 3 days is 0.7, and the probability that the lead time LTis 10 days is 0.3, in which the total sum of the probability h_(k)becomes 1.

The computation data calculation section 26 further includes aneffective lead time calculation section 46 in which an effective leadtime T_(i) is calculated from the lead time LT_(k) and the customer'srequired delivery time DT_(D). The effective lead time T_(i) is a valuethat denotes the period that has elapsed since an order of commodity hasbeen made or a production order has been released at the time point whenit has been predicted that commodity stock will fall below acorresponding reorder point until the shipment of the commodity or usethereof is enabled after delivery of the commodity or completion of themanufacturing of the commodity.

In the case where the lead time LT_(k) is longer than the customer'srequired delivery time DT_(j), the difference between the two isregarded as the effective lead time T_(i). On the other hand, in thecase where the lead time LT_(k) does not exceed the customer's requireddelivery time DT_(j), which denotes a state where the lead time isshorter than the customer's required delivery time and where it ispossible to always cope with the customer's required delivery time, theeffective lead time T_(i) becomes 0. That is, when LT_(K)>DT_(j),T_(i)=LT_(k)−DT_(j), and when LT_(K)≦DT_(j), T_(i)=0. In this case, theeffective lead time T_(i) denotes the number of days exceeding deliverytime. Note that the average number of days exceeding delivery time LL ofthe first embodiment is an average of the effective lead time T_(i).

As described above, the effective lead time T_(i) is calculated from theLT_(K) and DT_(j), and the LT_(K) and DT_(j) depend on the discretedistribution h_(k) and discrete distribution g_(j). Accordingly, theeffective lead time T_(i) also depends on the discrete distributiondefined by f_(i). Thus, the computation data calculation section 26includes an effective lead time probability distribution calculationsection 47 that calculates the discrete distribution f_(i) of theeffective lead time T_(i). The discrete distribution f_(i) iscalculated, for each effective lead time Ti, by multiplying the discretedistribution g_(j) of the required delivery time and the discretedistribution h_(k) of the lead time.

FIG. 8 is a table showing calculation results of the effective lead timeT_(i) in the case of FIGS. 6 and 7. The effective lead time T_(i)assumes six different values depending on the combination of DTs (1 to 3days) and LTs (3 and 10 days). Then, by multiplying h_(k) and g_(j) foreach effective lead time T_(i), the discrete distribution f_(i) of eacheffective lead time T_(i) is obtained. That is, the discretedistribution f_(i) can be represented by the following equation:

$\begin{matrix}{{f_{i} = {\sum\limits_{j,{k \in {Si}}}\; \left( {g_{j} \times h_{k}} \right)}}{{Si}\; = \; \left\{ {j,{{kT_{i}} = {{LT}_{k} - {DT}_{j}}}} \right\}}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack\end{matrix}$

As shown in the above equation, the discrete distribution f_(i) is thetotal sum of (g_(j)×h_(k)) for each combination of LT_(k) and DT_(J) inwhich Ti=LT_(k)−DT_(j). When, for example, there are a plurality of thecombinations that make Ti=3, such as “LT_(k)=5, DT_(j)=2”, “LT_(k)=6,DT_(j)=3”, and “LT_(k)=7, DT_(j)=4”, although the example shown in FIG.8 does not include combinations in which the T_(i) assumes the samenumber, the total sum of (g_(j)×h_(k)) for the above three case becomesa value of f_(i) in the case where T_(i)=3.

Further, the computation data calculation section 26 includes a marginallead time calculation section 48 that calculates a marginal lead timeL_(M) based on the effective lead time T_(i) and permissible stockoutrate α. The marginal lead time L_(M) is a minimum value of the effectivelead time T_(i) to be obtained after the cumulative value of theappearance probability f_(i) of the effective lead time T_(i) hasexceeded 1−α(=ratio of service S). That is, the marginal lead time L_(M)can be represented by the following equation:

$\begin{matrix}{L = {{\max \; T_{i}\mspace{14mu} {where}\mspace{14mu} {\sum\limits_{i = 1}^{n}\; f_{i}}} < \left( {1 - \alpha} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack\end{matrix}$

The safety coefficient calculation section 23 calculates the safetycoefficient k using the permissible stockout rate α that has been inputthrough the input unit 4. While the safety coefficient k is calculatedfrom the ratio of service S and safety coefficient table 16 in the firstembodiment, the safety coefficient k is calculated, in a more generalmanner, using an inverse function v(α) of the cumulative densityfunction of the demand probability distribution in this secondembodiment. The safety coefficient calculation section 23 firstlycalculates the demand probability distribution based on data of thesales/shipment DB 14 and creates the cumulative density functionthereof. The cumulative density function is an integral of the demandprobability distribution. The function value corresponding to a certaindemand denotes a probability that the demand larger (or smaller) thanthe certain demand amount appears.

The inverse function of the cumulative density function as above derivesthe demand from the appearance probability of the demand, and v(α)denotes the demand whose appearance probability is α. Accordingly, whenthe permissible stockout rate is used as the α, demand in which thepermissible stockout rate is α is derived. Further, the safetycoefficient calculation section 23 calculates the demand standarddeviation σ₀ based on the sales/shipment data. When the cumulativedensity function v(α) is divided by the demand standard deviation σ₀, avalue denoting how many times the demand in which the permissiblestockout rate is α is as large as the standard deviation σ₀ iscalculated. The calculated value is the safety coefficient k(k=v(α)/σ₀). Note that the ratio of service S (S=1−α) may be used inplace of the permissible stockout rate α.

The safety stock amount calculation section 24 calculates the safetystock amount ss based on the data calculated in the basic datacomputation section 21 and computation data calculation section 26 andthe safety coefficient k calculated in the safety coefficientcalculation section 23. The safety stock amount ss is calculated by thefollowing equation:

SS=k√{square root over (F_(D)Σf_(i) ²T_(i))}σ_(D)  [Equation 5]

Assuming that X: demand during procurement period, x_(i): demandcorresponding to effective lead time T_(i), x: demand during a unit ofperiod, and σ_(x): standard deviation of demand during procurementperiod, X is represented by [Equation 6], and the variance V(X) of X isrepresented by [Equation 7].

$\begin{matrix}{X = {\sum\limits_{i = 1}^{n}\; \left( {{P\left( T_{i} \right)} \times x_{i}} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack \\{{V(X)} = {V\left( {\sum\limits_{i = 1}^{n}\; \left( {{P\left( T_{i} \right)}^{2} \times x_{i}} \right)} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack\end{matrix}$

The [Equation 7] can be modified as [Equation 8] due to additivity ofvariance.

$\begin{matrix}{{V(X)} = {\sum\limits_{i = 1}^{n}\; \left\lbrack {{P\left( T_{i} \right)}^{2} \times {V\left( x_{i} \right)}} \right\rbrack}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack\end{matrix}$

The [Equation 8] can be modified as [Equation 9] by the definition ofvariance V(x_(i)) of x_(i). Further, when V(x), which is irrelevant toi, is taken out, the [Equation 9] is represented as [Equation 10].

$\begin{matrix}\begin{matrix}{{V(X)} = {\sum\limits_{i = 1}^{n}\; \left( {{P\left( T_{i} \right)}^{2} \times T_{i} \times {V(x)}} \right)}} \\{= {\left\lbrack {\sum\limits_{i = 1}^{n}\; \left( {{P\left( T_{i} \right)}^{2} \times T_{i}} \right)} \right\rbrack \times {V(x)}}}\end{matrix} & \begin{matrix}\begin{matrix}\begin{matrix}{\mspace{11mu} \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack} \\\;\end{matrix} \\\left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack\end{matrix} \\\;\end{matrix}\end{matrix}$

Accordingly, σ_(x) is represented as follows:

$\begin{matrix}\begin{matrix}{{\sigma \; x} = \sqrt{V(X)}} \\{= {\sqrt{\sum\limits_{i = 1}^{n}\; \left( {{P\left( T_{i} \right)}^{2} \times T_{i}} \right)} \times \sqrt{V(x)}}} \\{= {\sqrt{\sum\limits_{i = 1}^{n}\; \left( {{P\left( T_{i} \right)}^{2} \times T_{i}} \right)} \times \sigma_{D}}}\end{matrix} & \left\lbrack {{Equation}\mspace{14mu} 11} \right\rbrack\end{matrix}$

Therefore, when the [Equation 10] is assigned to the safety stock amountss=kσ_(x) with the demand frequency F_(D) taken into consideration, theabove [Equation 5] can be obtained.

The reorder point and the like calculation section 25 calculates thereorder point or order quantity based on the safety stock amount sscalculated in the safety stock amount calculation section 24. Under thefixed order quantity system, the reorder point and the like calculationsection 25 functions as a reorder point calculation section, where areorder point Q_(RO) is calculated by the following equations:

Q _(RO)=DA×L _(M) ×F _(D)+SS  [Equation 12]

Under the periodic ordering system, the reorder point and the likecalculation section 25 functions as an order quantity calculationsection, where an order quantity Q_(RO)′ is calculated(Q_(RO)′=commodity amount to be used in (LM+ordering cycleM))+SS−current stock amount−current order remaining amount).

In the calculation device having the configuration described above, thesafety stock amount ss is calculated along the procedure as describedbelow for obtaining the reorder point O and the like. As shown in FIG.5, firstly, the permissible stockout rate α (or ratio of service S) andordering cycle M are input in steps S11 and S12. The ordering cycle M isorder interval set in the periodic ordering system, and for example “30days” or the like is input as the ordering cycle M. Under the fixedorder quantity system, the ordering cycle M need not be input. As thepermissible stockout rate α, “5%” or the like is input.

When inputs of these values have been completed, the CPU 1 accesses thesafety stock amount calculation program 11 according to the controlprogram 13 and accordingly calculates various fundamental data. In orderto calculate the safety stock amount ss, the safety stock amountcalculation program 11 allows the CPU 1 to function as the delivery timeprobability distribution calculation section 44, lead time probabilitydistribution calculation section 45, effective lead time calculationsection 46, effective lead time probability distribution calculationsection 47, and safety stock amount calculation section 24.

The CPU 1 calculates the safety coefficient k, demand standard deviationσ_(D) per unit of period, demand average DA per unit of period, anddemand frequency F_(D) in steps S13 to S16. The calculated values arestored in the work area 12 and used in the following computations.

As described above, the safety coefficient k is calculated by the safetycoefficient calculation section 23 based on the cumulative densityfunction v(α) and standard deviation α₀ (k=v(α)/σ₀). Alternatively, thesafety coefficient table may be referred to as the first embodiment. Thedemand standard deviation σ_(D) per unit of period, demand average DAper unit of period, and demand frequency F_(D) are calculated by thebasic data computation section 21 based on data of the sales/shipment DB14.

After the fundamental data have been calculated, the CPU 1 reads in thecustomer's required delivery time DT_(j) and lead time LT_(K) from theorder DB 15 in steps S17 and S18. After that, various computation dataare calculated using the above values. Firstly, in step S19, thediscrete distribution g_(j) of the customer's required delivery timeshown as an example in FIG. 6 is calculated. Further, in step 20, thediscrete distribution h_(k) of the lead time as shown in FIG. 7 iscalculated.

The flow advances to step S21 and the CPU 1 calculates the effectivelead time T_(i) using the discrete distribution g_(j) of the customer'srequired delivery time and discrete distribution h_(k) of the lead time.As described above, when LT_(K)>DT_(j), T_(i)=LT_(K)−DT_(j), and whereaswhen LT_(K)≦DT_(j), T_(i)=0. After that, the discrete distribution f_(i)of the effective lead time T_(i) is calculated based on the discretedistribution g_(j) of the customer's required delivery time, discretedistribution h_(k) of the lead time and effective lead time T_(i) byusing [Equation 3] (step S22).

After the effective lead time T_(i) and discrete distribution f_(i)thereof have been calculated, the marginal lead time LM is calculated asshown in the [Equation 4] using the discrete distribution f_(i) andpermissible stockout rate α (step S23). The flow advances to step S24and the safety stock amount calculation section 24 calculates the safetystock amount ss based on the above [equation 5]. FIG. 9 is a tableshowing calculation results of (f_(i) ²·T_(i)) within the square root ofthe [equation 5] using the discrete distribution f_(i) of the effectivelead time T_(i) obtained in FIG. 8 and the cumulative value of discretedistribution f_(i).

As to the marginal lead time LM, assuming, in the example of FIG. 9,that permissible stockout rate α=5%, the minimum effective lead timeT_(i) to be obtained after the cumulative value f_(i) has exceeded1−α=0.95 is 9, with the result that the marginal lead time LM=9. As tothe safety stock amount ss in this example, assuming that demandfrequency F_(D)=0.5, safety coefficient k=1.65, and demand standarddeviation σ_(D) per unit of period=30 and these values are assigned tothe [Equation 5], ss=1.65×(0.5×0.5816)^(1/2)×30=26.693.

After the safety stock amount ss has been calculated as described above,the flow advances to step S25, where the reorder point and the likecalculation section 25 calculates the reorder point Q_(RO) or orderquantity using the above [Equation 12]. In the case of the aboveexample, assuming that demand average DA per unit of period=100,Q_(RO)=100×9×0.5+26.693=476.693. This means that the safety stock amountwith a permissible stockout rate α of 5% or less is 26.693, and thereorder point needed to maintain this value in the abovementionedcondition is 476.693. That is, it can be understood from the result thatwhen the stock amount of a certain commodity has fallen below 476, thecommodity should be ordered.

Whereas, according to the conventional safety stock amount calculationmethod (Equation 1: ss=k×σ′), ss=1.65×(0.5×10)^(1/2)×30=110.69. That is,the use of the [Equation 5] can reduce the safety stock amount by about¼. Further, when the reorder point Q_(RO) is calculated according to theconventional calculation method, Q_(RO)=10×100+110.69=1110.69. That is,the use of the [Equation 5] can reduce the reorder point by ½ or less.

As described above, the safety stock amount calculation method anddevice according to the second embodiment calculates the appearanceprobability related to the customer's required delivery time and thelead time as well as calculates the appearance probability of theeffective lead time using the above calculated values and finallycalculates the safety stock amount based on the effective lead time andthe appearance probability thereof. As a result, it is possible todesign a more general inventory management system being based on aprojected inventory as compared to the first embodiment.

In the above case, where the discrete distribution g_(j) of the requireddelivery time or discrete distribution h_(k) of the lead time isunknown, the safety stock amount ss may be obtained by the followingequation:

SS=k√{square root over (L×F _(D))}×σ_(D) ×M  [Equation 13]

In the [Equation 13], L=_(max)T_(i)=LT_(max)−DT_(min) (minimum deliverytime is subtracted from max lead time) is satisfied. Further, M is aprobability that the purchase order that causes a commodity speculativeproduction or procurement of the commodity to be needed is generatedbecause it is impossible to make it for the purchase order in the casewhere an order of the commodity is made or manufacturing of thecommodity is started even immediately after the purchase order. The Mcorresponds to the short delivery time ratio Pb of the first embodiment,and may be calculated based on the past record or experimental values.

The [Equation 13] corresponds to the case where (T₁=L, f₁=M), (T₂=0,f₂=1−M) in the [Equation 5]. This means that the probability that theeffective lead time is L is M and otherwise the lead time is shorterthan the delivery time (delivery delay does not occur). The equationthat uses the average number of days exceeding delivery time LL in placeof L=_(max)T_(i) is the [Equation 2] of the first embodiment. That is,the [Equation 2] and [Equation 13] each corresponds to a particularsolution of the [Equation 5].

It goes without saying that the present invention is not limited to theabove embodiments, and various changes may be made without departingfrom the scope of the invention.

For example, each of the values such as Pb described in the aboveembodiments or each of the examples of the second embodiment shown inFIGS. 6 to 9 is merely one example, and the calculation method andcalculation device according to the present invention are not limited tothe above. Further, while the method of the present invention isutilized as a part of an ERP package in the above example, the methodand device of the present invention can independently be used.

Further, the present invention is applicable to ordering methods otherthan “periodic ordering system” or “fixed order quantity system”. Forexample, the present invention can be applied to various methods such asan intermediate method between the “periodic ordering system” and “fixedorder quantity system” that previously sets the maximum and minimumstock amounts and orders commodity by the difference between the maximumstock amount and the stock amount at the ordering moment at the timepoint when the stock amount has fallen below the reorder point (minimumstock amount).

Further, as the representative value LL of the difference between thelead time L and customer's required delivery time, the average number ofdays exceeding delivery time, which is an arithmetic average of thedifference between the two, is used in the above embodiments.Alternatively, however, various average values such as geometric averageor harmonic average, median, mode, experimental values, or the like ofthe difference between the lead time L and customer's required deliverytime can be used. Similarly, as to the demand average A or DA, otherrepresentative values that represent its distribution can be used. Thatis, as the demand average A or DA, not only arithmetic average, but alsogeometric average or harmonic average can be used. In addition, medianand mode can be used in place of the above average values. Also in thiscase, experimental values can be used.

Further, the present invention is also applicable to the case where thedemand does not exhibit normal distribution. In this case, distributionfunction of the demand is calculated, and the safety coefficient k thatsatisfies a desired ratio of service S is calculated based on thecalculated distribution function, for example.

Further, while both the appearance probability of the lead time LT_(K)and the appearance probability of the customer's required delivery timeDT_(j) are represented by discrete distributions in the secondembodiment, one of the two may be represented by a continuousdistribution. The use of an increased number of days as samples of thelead time LT_(K) or customer's required delivery time DT_(j) may resultin an enormous number of combinations of the effective lead time T_(i),increasing calculation load for the discrete distribution f_(i). In sucha case, representative values may appropriately be used to calculate thediscrete distribution f_(i). In this time, a so-called Monte Carlosimulation may be performed by using a random number table or the like.

In the above embodiments, the demand standard deviation (standarddeviation of demand amount per unit of period) is used to calculate thesafety stock amount and the like. Alternatively, however, it is possibleto use, as the standard deviation, not only statistical standarddeviation but also a value that indicates the uncertainty of the demand.For example, it is possible to use a square root of the value obtainedby diving the square-sum of the prediction error between individualdemand and corresponding predicted demand by (n−1) (number of dataitems−1).

The safety stock amount calculation method according to the presentinvention that calculates the safety stock amount SS based on the demandstandard deviation σ for a certain commodity, the inventory adjustmentperiod N calculated from the lead time L of the commodity or itscomponents, and the safety coefficient k that denotes the level of theratio of service S for demand, corrects the inventory adjustment periodN with the average number of days exceeding delivery time LL as well ascalculates the safety stock amount SS using the short delivery timeratio Pb. Therefore, it is possible to set a practical stock amount thatmeets occurrence of the case where a response to the customer's ordermust be made with the safety stock. Since this method is a calculationmethod that uses achievement data of average number of days exceedingdelivery time LL and the short delivery time ratio Pb, it is possible tocope with the case where an order of commodity and the like is madebased on a projected inventory, making it possible to adequately set thesafety stock amount of commodity and the like in the ERP package or thelike.

Further, the safety stock amount calculation method according to thepresent invention calculates the appearance probability related to thecustomer's required delivery time and the lead time as well ascalculates the appearance probability of the effective lead time usingthe above calculated values and finally calculates the safety stockamount based on the effective lead time and the appearance probabilitythereof. As a result, it is possible to design a more general inventorymanagement system being based on a projected inventory. Since the methodof the present invention is a calculation method that uses achievementdata, it is possible to cope with the case where an order of commodityand the like is made based on a projected inventory, making it possibleto adequately set the safety stock amount of commodity and the like inthe ERP package or the like.

1-30. (canceled)
 31. A safety stock amount calculation method,comprising: storing, in a storage unit that includes a non-transitorycomputer-readable recording medium, a safety stock amount calculationprogram executable by a processor; calculating, using the processor, anappearance probability of a certain delivery time based on a deliverytime for a certain commodity required by a customer and frequency;calculating, using the processor, an appearance probability of a leadtime of the commodity or components of the commodity; calculating, usingthe processor and based on the customer's required delivery time andlead time, an effective lead time T_(i) that denotes a period between atime when it has been predicted that the commodity stock will fall belowa corresponding reorder point and a time when the commodity has becomeavailable after the commodity had been ordered based on the predictionthat the commodity stock would fall below a corresponding reorder point;calculating, using the processor, an appearance probability of theeffective lead time T_(i) based on the appearance probability of thecustomer's required delivery time and the appearance probability of thelead time; and calculating, using the processor, a safety stock amountss based on a demand standard deviation σ_(D) for the commodity per unitof period, a safety coefficient k that denotes the level of a ratio ofservice S for demand, the effective lead time T_(i) and the appearanceprobability of the effective lead time.
 32. The reorder pointcalculation method of claim 31, further comprising: calculating areorder point Q_(RO) based on a safety stock amount ss calculated, arepresentative value DA including any one of an average value, median,mode and experimental value of a demand per unit of period, and amarginal lead time L_(M) that denotes a minimum value of the effectivelead time to be obtained after the cumulative value of the appearanceprobability of the effective lead time T_(i) has exceeded the ratio ofservice S.
 33. The reorder point calculation method according to claim32, further comprising: calculating the reorder point Q_(RO) by using ademand frequency F_(D) that denotes an appearance probability of theperiod during which demand per unit of period is not 0 in addition tothe safety stock amount ss, representative value DA of a demand, andmarginal lead time L_(M).
 34. A safety stock amount calculation method,comprising: storing, in a storage unit that includes a non-transitorycomputer-readable recording medium, a safety stock amount calculationprogram executable by a processor; calculating, using the processor, anappearance probability of a certain delivery time based on a deliverytime for a certain commodity required by a customer and frequency tocreate a probability distribution g_(j) of the customer's requireddelivery time; calculating, using the processor, an appearanceprobability of a lead time of the commodity or components of thecommodity to create a probability distribution h_(k) of the lead time;calculating, using the processor and based on the customer's requireddelivery time and lead time, an effective lead time T_(i) that denotes aperiod between a time when it has been predicted that the commoditystock will fall below a corresponding reorder point and a time when thecommodity has become available after the commodity had been orderedbased on the prediction that the commodity stock would fall below acorresponding reorder point; calculating, using the processor, anappearance probability of the effective lead time T_(i) based on theprobability distribution g_(j) of the customer's required delivery timeand the probability distribution h_(k) of the lead time to create aprobability distribution f_(i) of the effective lead time; andcalculating, using the processor, a safety stock amount ss based on ademand standard deviation σ_(D) for a certain commodity per unit ofperiod, a safety coefficient k that denotes the level of a ratio ofservice S for demand, the effective lead time T_(i) and the probabilitydistribution f_(i) of the effective lead time.
 35. The safety stockamount calculation method according to claim 34, wherein the step ofcalculating the safety stock amount ss calculates the safety stockamount ss using the following equation:SS=k√{square root over (Σf_(i) ²T_(i))}σ_(D)
 36. The safety stock amountcalculation method according to claim 34, wherein the step ofcalculating the safety stock amount ss further uses a demand frequencyF_(D) that denotes an appearance probability of the period during whichdemand per unit of period is not
 0. 37. The safety stock amountcalculation method according to claim 34, wherein at least one of theprobability distribution of g_(j) of the customer's required deliverytime and the probability distribution h_(k) of the lead time is adiscrete probability distribution.
 39. A reorder point calculationmethod of claim 34, further comprising: calculating a reorder pointQ_(RO) based on a safety stock amount ss calculated, a representativevalue DA including any one of an average value, median, mode andexperimental value of a demand per unit of period, and a marginal leadtime L_(M) that denotes a minimum value of the effective lead time to beobtained after the cumulative value of the appearance probability of theeffective lead time T_(i) has exceeded the ratio of service S.
 40. Thereorder point calculation method according to claim 34, furthercomprising: calculating the reorder point Q_(RO) by further using ademand frequency F_(D) that denotes an appearance probability of theperiod during which demand per unit of period is not 0 in addition tothe safety stock amount ss, representative value DA of a demand, andmarginal lead time L_(M).